Explain step-up and step-down transformer operation

Ontario Grade 11 Physics

Electricity and Magnetism

Ontario Grade 11 Physics — F3.8

A transformer changes the voltage of alternating current. It can raise voltage or lower it, depending on how many turns of wire are in each coil. To explain its operation, we will track energy transfer between two coils and use a simple model for their voltage and current. The lesson focuses on step-up and step-down operation.

What you will learn

Describe the main parts of a transformer and the role of changing current.
Use the turns ratio to compare primary and secondary voltage.
Explain how current changes in an ideal step-up or step-down transformer.
Check whether a calculated transformer result makes physical sense.

1. The system and the needed ideas

The physical system is a transformer with two coils of wire. The input coil is called the primary coil. The output coil is called the secondary coil. A magnetic core sits through or between the coils. The core helps guide the magnetic field from one coil toward the other.

A coil is wire wound in loops. Each loop is one turn. The number of turns in the primary is

N_p

; the number in the secondary is

N_s

. The input voltage and current are

V_p

and

I_p

. The output voltage and current are

V_s

and

I_s

. Voltage is measured in volts (V), current in amperes (A), and the number of turns is a count with no unit.

A transformer operates with alternating current (AC). AC repeatedly changes size and direction. That changing current produces a changing magnetic field in the core. A magnetic field is the region where magnetic effects can act. Its changing strength through the secondary coil produces a voltage there. This production of voltage by a changing magnetic field is called electromagnetic induction.

The coils are not electrically joined to each other in the basic transformer model. Energy is transferred from the input coil to the output coil through the changing magnetic field. A steady direct current (DC) does not keep changing, so after the brief switch-on change it does not provide the ongoing changing field needed for transformer operation.

Primary means input; secondary means output.
A continuing change in current and magnetic field is needed.
The core guides the changing magnetic field between the coils.

2. Turns ratio and voltage change

For a simple ideal transformer, the voltage ratio matches the turns ratio. Ideal means we treat energy losses as negligible. The model lets us explain the main operation without details about heating or other losses.

Compare secondary turns with primary turns. If the secondary has more turns, the secondary voltage is higher: this is a step-up transformer. If the secondary has fewer turns, the secondary voltage is lower: this is a step-down transformer. If the turn counts are equal, the model predicts equal voltages.

The sign convention here is to write input and output voltage magnitudes as positive values. AC voltage itself reverses direction over time, so these positive values describe its size, not a fixed direction of current. In the voltage-ratio equation, the subscripts identify the coils; they are not signs.

To use the equation, identify the known values and the unknown. Keep voltage in volts and compare turn counts as a ratio. Since turns are counts, the ratio has no unit. The resulting voltage has the same unit as the voltage supplied.

\frac{V_s}{V_p}=\frac{N_s}{N_p}

More secondary turns means a higher secondary voltage.
Fewer secondary turns means a lower secondary voltage.
Use voltage magnitudes with the stated input-output labels.

3. Current change and a useful check

In the ideal model, energy transferred each second is conserved. Electrical power is the rate of energy transfer, and for a coil it is found by multiplying voltage by current. Therefore, when voltage increases, current decreases by the corresponding ratio. When voltage decreases, current increases by the corresponding ratio.

This current relationship is a model for an ideal transformer. A real transformer can lose some energy, so its input and output powers are not exactly equal. For Grade 11 calculations here, use the ideal relationship when the question says ideal or gives no loss information.

Current is measured in amperes (A). As with voltage, the current values in the ratio describe magnitudes. They do not state a fixed direction, because the currents in an AC circuit reverse over time. The equations use positive magnitudes for the input and output.

A good check is to compare the turns and voltage first, then check current in the opposite sense. A step-up transformer should have a larger output voltage and a smaller output current in the ideal model. A step-down transformer should have a smaller output voltage and a larger output current. This check can reveal a reversed ratio or a misplaced subscript.

V_p I_p=V_s I_s

For an ideal transformer, input power equals output power.
A voltage increase pairs with a current decrease.
Check that current changes in the opposite sense to voltage.

Worked example

Finding the output voltage of a step-up transformer

An ideal transformer has 400 turns on its primary coil and 1,600 turns on its secondary coil. The primary voltage is 12 V. Find the secondary voltage.

Set up the system
The transformer coils are the system. Treat voltage as a positive magnitude, with the primary as input and the secondary as output. The known values are $N_p=400$ , $N_s=1600$ , and $V_p=12\,\mathrm{V}$ . The unknown is $V_s$ .
Apply the turns ratio
For an ideal transformer, secondary voltage divided by primary voltage equals secondary turns divided by primary turns. Rearrange to find the output voltage.
$V_s=V_p\frac{N_s}{N_p}$
Substitute and calculate
The turns ratio is four, so the output voltage is four times the input voltage. Keep the voltage unit in the calculation.
$V_s=(12\,\mathrm{V})\frac{1600}{400}=48\,\mathrm{V}$

Answer: The secondary voltage is

48\,\mathrm{V}

, to two significant figures.

Check: The secondary has four times as many turns, so a voltage four times as large is reasonable. The answer is positive because the stated voltage is a magnitude, and its unit is volts.

Worked example

Finding turns in a step-down transformer

A transformer has 900 turns on its primary coil. It lowers a 120 V input to a 24 V output. Find the number of secondary turns.

Define the quantities
The transformer coils are the system. Use positive voltage magnitudes, with the primary as input and secondary as output. The known values are $N_p=900$ , $V_p=120\,\mathrm{V}$ , and $V_s=24\,\mathrm{V}$ . The unknown is $N_s$ .
Rearrange the model
The voltage ratio equals the turns ratio. Multiply the primary turns by the secondary-to-primary voltage ratio to find the secondary turns.
$N_s=N_p\frac{V_s}{V_p}$
Substitute and calculate
The output voltage is one-fifth of the input voltage, so the secondary has one-fifth as many turns as the primary.
$N_s=(900)\frac{24\,\mathrm{V}}{120\,\mathrm{V}}=180$

Answer: The secondary coil has 180 turns.

Check: Turns are a count, so there is no unit to report. The output voltage is lower than the input voltage, and the result has fewer secondary turns than primary turns, as a step-down transformer should.

Worked example

Finding output current in an ideal step-down transformer

An ideal transformer changes 240 V at the primary to 60 V at the secondary. The primary current is 0.50 A. Find the secondary current.

Identify the system and values
The transformer is the system. Treat current and voltage as positive magnitudes. The primary is input and the secondary is output. The known values are $V_p=240\,\mathrm{V}$ , $V_s=60\,\mathrm{V}$ , and $I_p=0.50\,\mathrm{A}$ . The unknown is $I_s$ .
Use ideal power transfer
For an ideal transformer, input power equals output power. Since power is voltage multiplied by current, rearrange to find the secondary current.
$I_s=\frac{V_p I_p}{V_s}$
Substitute and calculate
Use volts and amperes throughout. The voltage drops by a factor of four, so the current rises by that factor in the ideal model.
$I_s=\frac{(240\,\mathrm{V})(0.50\,\mathrm{A})}{60\,\mathrm{V}}=2.0\,\mathrm{A}$

Answer: The secondary current is

2.0\,\mathrm{A}

, to two significant figures.

Check: The output voltage is one-quarter of the input, so the ideal output current is four times the input current. The units reduce to amperes, and a larger output current is reasonable for a step-down transformer.

Common mistakes and how to avoid them

Calling a transformer step-up because its primary coil has more turns.

Correction: Compare secondary turns with primary turns. More secondary turns make it step-up; fewer secondary turns make it step-down.

Using the primary-to-secondary turns ratio for the secondary-to-primary voltage ratio.

Correction: Keep the subscripts in matching order: secondary over primary for both voltage and turns.

Assuming a transformer continuously changes a steady DC voltage.

Correction: Transformer operation needs a changing current and changing magnetic field. A steady DC current does not maintain that ongoing change.

Expecting output current to increase whenever output voltage increases.

Correction: In the ideal model, voltage and current change in opposite senses because input and output power are equal.

Lesson summary

A changing primary current creates a changing magnetic field that induces voltage in the secondary coil.
The voltage ratio equals the turns ratio for an ideal transformer.
More secondary turns give a step-up transformer; fewer give a step-down transformer.
In the ideal model, voltage and current change in opposite senses, while input and output power are equal.
Check labels, units, significant figures, and whether the result matches step-up or step-down operation.

Check your understanding

Question 1

A primary coil has 500 turns and the secondary has 2,000 turns. What happens to the voltage magnitude in the ideal model?

It becomes four times as large.
It becomes one-quarter as large.
It stays the same.
correctIndex":0,"explanation":"The secondary-to-primary turns ratio is $2000/500=4$ . The voltage ratio has the same value, so this is a step-up transformer."}

Show answer and explanation

It becomes four times as large.

The secondary-to-primary turns ratio is

2000/500=4

. The voltage ratio has the same value, so this is a step-up transformer.

Question 2

An ideal transformer steps voltage down. What happens to the current magnitude?

It decreases in the same ratio as the voltage.
It increases in the opposite ratio to the voltage.
It must remain unchanged.
correctIndex":1,"explanation":"Ideal input and output power are equal. A lower output voltage therefore pairs with a higher output current."}

Show answer and explanation

It increases in the opposite ratio to the voltage.

Ideal input and output power are equal. A lower output voltage therefore pairs with a higher output current.

Question 3

Why does a steady DC current not provide ongoing transformer operation?

It does not keep changing the magnetic field.
It always has a greater voltage than AC.
It gives the secondary coil more turns.
correctIndex":0,"explanation":"A transformer needs a continuing change in magnetic field to induce voltage in the secondary. Steady DC does not provide that continuing change."}

Show answer and explanation

It does not keep changing the magnetic field.

A transformer needs a continuing change in magnetic field to induce voltage in the secondary. Steady DC does not provide that continuing change.

Key terms

Alternating current (AC): Electric current that repeatedly changes size and direction.
Primary coil: The transformer coil connected to the input.
Secondary coil: The transformer coil that provides the output.
Turn: One loop of wire in a coil.
Electromagnetic induction: The production of voltage by a changing magnetic field.
Ideal transformer: A simplified transformer model in which energy losses are negligible.
Step-up transformer: A transformer whose secondary voltage is greater than its primary voltage.
Step-down transformer: A transformer whose secondary voltage is less than its primary voltage.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Physics (SPH3U), expectation F3.8. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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